Method of initializing a communication system with different bandwidth receivers and transmitters

ABSTRACT

A method of communicating across a channel includes receiving information having a known bandwidth and a known spectrum. The information is preferably in the form of a multicarrier modulated signal, e.g., a DMT signal. In one aspect, this information is received at a receiver having a reduced channel bandwidth. An aliasing spectrum can be calculated based on the known spectrum and the frequency difference between the known bandwidth and the reduced-channel bandwidth. The received information can then be modified based upon the aliasing function to compensate for alias distortion. For example, the received information can be modified by modifying the noise component or signal-to-noise ratio of the received information.

FIELD OF THE INVENTION

This invention relates generally to communication systems andspecifically to a method of initializing a communication system withdifferent bandwidth receivers and transmitters.

BACKGROUND OF THE INVENTION

Communication systems are used to transfer information from one locationto another. The content and format of this information can vary greatlydepending upon the type of system and the application. For example,there is a great need to communicate digital information such as data,voice, video and others. Depending upon the channel used, thisinformation is often transmitted in analog form.

FIG. 1 illustrates a simple block diagram of a conventional receiver 10.An analog signal is received at analog receiver 12. The signal is thendigitized in analog-to-digital converter (ADC) 14. The digitalinformation can then be processed using a digital processor 16.

As is well known, the Nyquist theory states the minimum sampling raterequired to turn an analog signal into an accurate digitalrepresentation. Specifically, the sampling rate must be at least twicethat of the highest component of the analog frequency in order toaccurately reproduce the sampled signal. FIGS. 2 a-2 c illustrate thispoint.

FIG. 2 a shows the frequency spectrum of an arbitrary analog signal. Asshown in FIG. 2 b, when the signal is sampled, an image spectrum will begenerated. The image spectrum will be a mirror image of the originalspectrum with the sample frequency serving as the axis of symmetry. Thisresult leads to the Nyquist theory. If the sample frequency is greaterthan the maximum frequency of the original spectrum, the originalspectrum will be retrievable. If, however, the sample frequency is lessthan the maximum frequency, the image spectrum will overlap the originalspectrum, as shown in FIG. 2 c. This effect is known as aliasing. Theportion of the image spectrum that overlaps the original spectrum,referred to as the aliasing spectrum or alias band herein, will distortthe original spectrum and prevent accurate reproduction.

SUMMARY OF THE INVENTION

In one aspect, the present invention provides a technique for evaluatingthe effect of the aliasing spectrum and compensating for this effect.This technique can be utilized, for example, during the initializationsequence of a communication system when each device is evaluating thecommunication link and determining the rate and bandwidth that will beused.

A preferred embodiment of the present invention provides a method ofcommunicating across a channel includes receiving information having aknown bandwidth and a known spectrum. The information is preferably inthe form of a multicarrier modulated signal, e.g., a Discrete Multitone(DMT) signal. In one aspect, this information is received at a receiverhaving a reduced channel bandwidth. An aliasing spectrum can becalculated based on the known spectrum and the frequency differencebetween the known bandwidth and the reduced-channel bandwidth. Thereceived information can then be modified based upon the aliasingfunction to compensate for alias distortion. For example, the receivedinformation can be modified by modifying the noise component orsignal-to-noise ratio of the received information.

This method can be used, for example, to initialize the channel. Duringan initialization sequence, known symbols are transferred from one modemto the other. These known symbols can be used to estimate the effect ofthe alias channel on the reduced channel. For example, a correctedreduced channel signal-to-noise ratio can be estimated. This correctedvalue will more accurately predict the operability of the channel. Thisincrease in accuracy leads to an increase in available bandwidth andtherefore a more efficient system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simple block diagram of a known receiver;

FIGS. 2 a-2 c illustrate the Nyquist theory;

FIG. 3 illustrates the spectrum of an asymmetric DSL channel;

FIG. 4 illustrates the situation where a transmitter of one bandwidthtransmits information to a receiver of a smaller bandwidth;

FIG. 5 illustrates the aliasing effect of a receiver as in FIG. 4;

FIGS. 6 a and 6 b illustrate the frequency utilization of a reduced rateversus a full rate DMT based modem; and

FIG. 7 illustrates a method of communicating across a channel inaccordance with an embodiment.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The making and use of the various embodiments are discussed below indetail. However, it should be appreciated that the present inventionprovides many applicable inventive concepts which can be embodied in awide variety of specific contexts. The specific embodiments discussedare merely illustrative of specific ways to make and use the invention,and do not limit the scope of the invention.

The present invention can be utilized in a number of contexts. Forexample, the preferred embodiment communication system is a digitalsubscriber line (DSL) system. As a result, the present invention willfirst be described in the context of such a system. It should berecognized, however, that the inventive concepts can apply to a numberof other systems as well.

DSL is a technology that dramatically increases the digital capacity ofordinary telephone lines (the local loops) into the home or office. DSLspeeds are tied to the distance between the customer and the telephonecompany central office (CO). DSL is geared to two types of usage.Asymmetric DSL (ADSL) is for Internet access, where fast downstream isrequired, but slow upstream is acceptable. Symmetric DSL is designed forshort haul connections that require high speed in both directions.

An advantage of a DSL system is that it can operate on an existingtelephone system simultaneously with voice traffic. This feature isaccomplished by apportioning a different range of frequencies to thedata traffic. This spectrum is different than the spectrum alreadyassigned to the voice. An example of an ADSL spectrum is shown in FIG.3, where the voice occupies the baseband portion of the line and theupstream (US) and downstream (DS) signals utilize a high frequency band.This system is asymmetric because the downstream spectrum (i.e., from COto remote terminal or RT) has a greater bandwidth than the upstreamspectrum (i.e., from RT to CO).

Different standards have evolved that define the bandwidth that will beutilized between the two spectra. For example, the G.dmt standarddefines a downstream bandwidth of 1104 kHz while the G.lite standarddefines a downstream bandwidth of 552 kHz If two modems arecommunicating, they will only be able to utilize the bandwidth availableto the smaller of the two. For example, when a G.dmt modem communicateswith a G.lite modem, the downstream communication will only occur withina 552 kHz band.

Multicarrier communication is a technology in which the availabletransmission bandwidth is conceptually divided into a number ofsub-channels such that the channel response is approximately constantover each of the sub-channels. An orthogonal basis of signals is used tomodulate the transmitted data over the different sub-channels. A cyclicprefix can be used to maintain sub-carrier orthogonality and reduceinterblock interference.

Multicarrier modulation technology is used to achieve data transmissionrates close to the channel capacity. Several applications likeaudio/video broadcasting, cable television, xDSL modems, mobile localarea networks and future generation wideband cellular systems use (orplan to use) multicarrier modulation methods. The present invention isespecially used with multicarrier modulation technology.

When the modems use multicarrier modulation scheme, such as digitalmultitone (DMT), adjusting the bandwidth is a relatively straightforwardprocess. DMT modulation uses a number of carrier signals spaced infrequency. The bandwidth of the entire system can be adjusted by usingmore or fewer of the sub-carriers. This same principle applies in othermulticarrier modulation schemes.

An initialization or training procedure is used to determine theproperties of the two devices in the system. These properties includethe available bandwidth. FIG. 4 illustrates a situation where a firstmodem (e.g., CO) sends information to the second (e.g., RT) over achannel. The second modem knows the content of the initializationsequence and determines the information that was successfullytransmitted. Based on the results, the two units will determine anappropriate operating regime.

One of the interoperability issues between multicarrier communicationsystems using different overlapping bandwidths for data transmission isthe inaccurate estimate of sub-channel signal-to-noise ratios (SNRs)obtained during the training phase due to the aliased signal energy.This effect is illustrated in FIG. 5.

In FIG. 5, the original spectrum is labeled with reference numeral 20and the image spectrum is labeled with reference numeral 22. In thisexample, the original spectrum has a bandwidth of B. Due to aliasing,however, the usable bandwidth has been reduced to a*B (where 0<a<1). Thealiasing spectrum (denoted by shaded portion 24) uses the remainder tothe otherwise available bandwidth.

This effect can significantly reduce the performance and in certaincases even prevent a data connection from being established. Forexample, in ADSL modems there are two distinct standards that specifydownstream data transmission from the central office modem to the usermodem over different bandwidths of 138 KHz-1.104 MHz (full-band) and 138KHz-552 KHz (half-band).

When a reduced-band user modem connects up to a full-band central officemodem the out-of-band aliased energy transmitted from the central officemodem during training sets the receive noise floor and hencesignificantly reduces the achievable performance as estimated duringtraining (See FIG. 2). At the end of the training phase, however, theuser modem indicates to the central office modem not to transmit dataover the out-of-band frequency region, which includes the aliasingregion 24. This indication was made based on the estimated SNRs, whichare impacted by the aliasing effect. Hence, in reality the achievabledata rate is much higher than that estimated during the training phase(since there is no aliased signal energy during data transfer).

The present invention includes embodiments that can be used to getaround this problem. For example, in one embodiment the aliased signalcomponents are eliminated in the user modem over the differentsubchannels (since the user modem is aware of the training signalstransmitted by the central office modem) and then subtracting out thealiased signal energy during the SNR estimation phase. As mentionedabove, the proposed alias cancellation method is general enough to beapplied to any wireline or wireless multicarrier communications scenario(e.g., using DMT, OFDM, and others).

The following paragraphs provide a specific implementation of apreferred embodiment of the present invention to illustrate theusefulness of the invention.

This example provides methods for signal-to-noise ratio (SNR) estimationfor reduced-rate remote terminal (RT) receivers operating against afull-rate central office (CO) transmitter. The techniques will bedescribed with reference to a system that uses the discrete multi tone(DMT) modulation scheme. The terminology reduced versus full-rate refersto the number of frequency tones used in the DMT modulation, i.e., thereduced-rate modem uses a fraction α of the frequency tones that areavailable in the full-rate modem.

A typical scenario is that of a half-rate RT that only uses the firsthalf of the frequency tones available to the full-rate CO that itcommunicates to. For example, this is the case for a G.lite RT (asshown, for example, in U.S. Pat. No. 6,044,107) communicating against aG.dmt CO (as shown, for example, in F. van der Putten (ed.), “G.dmt-bis:draft recommendation,” ITU Telecommunications Standardization SectorStudy Group 15 Question 4, August 2000) in the absence of a handshakeprocedure like the procedure shown by T. Cole (ed.), “G.lite-bis: draftrecommendation,” ITU Telecommunications Standardization Sector StudyGroup 15 Question 4, August 2000. Each of these three references isincorporated herein by reference.

During training, the full-rate CO transmits a full band signal that isalso known by the RT. The half-rate receiver attempts to filter theupper half of the transmitted spectrum out. As described above, however,this is not a perfect operation. The part of the upper band of thereceived spectrum that makes it through the filter will show in thelower band as alias and will be considered as interference. Therefore,the SNR computation performed during training will be affected. Itshould be pointed out that during show time operation (after training)this will not be a problem, since the upper tones will have an SNR lowerthan the minimum and will not be used. One aspect of this inventionprovides a solution to this problem and proposes approaches toaccurately estimate the SNR in the presence of the inevitable alias.

In the discussion that follows, it is assumed that the reduced-rate andfull-rate modems have αN and N frequency tones, respectively, with α<1.This is illustrated in FIGS. 6 a and 6 b. Two frequency indexes areused. The first one represents the reduced-rate channel and is denotedby k₁ε[0, αN−1]. The second index, denoted by k₂∈[αN, N−1], encompassthose channels in the upper portion of the full-rate channel, i.e., thealias channel. These indexes are related by k₂=N−1−k₁. Thus, thereduced-rate and alias channels are represented in the frequency domainas H(k₁) and H(k₂), respectively. The frame index is denoted by n andthe received and training symbols, in the frequency domain, are denotedby Y(k, n) and X(k, n), respectively. With these definitions, thereceived signal is given byY(k ₁ , n)=H(k ₁)X(k ₁ , n)+H(X ₂)X(k ₂ , n)+V(k ₁ , n),  (1)where V represents the noise component.

In one aspect, the goal is to estimate the reduced-rate and aliaschannels based on the received signal Y(k₁, n) and knowledge of thefull-band transmitted signal, i.e., X(k₁, n) and X(k₂, n). In whatfollows, two methods are presented for estimating the reduced-rate andalias channels.

For truly uncorrelated training data (both with respect to the frame andtone indexes), the reduced-rate channel can be estimated as

$\begin{matrix}{{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack} = {E\left\lbrack {{{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} + {H\left( k_{2} \right)}} \right.}} & \\{\left. {{{X\left( {k_{2},n} \right)}X*\left( {k_{1},n} \right)} + {{V(n)}X*\left( {k_{1},n} \right)}} \right\rbrack} & \\{= {E\left\lbrack {{{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} +} \right.}} & {(2)} \\{\left. {{H\left( k_{2} \right)}{X\left( {k_{2},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack} & \\{= {E\left\lbrack {{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack}} & {(3)} \\{{= {2{H\left( k_{1} \right)}}},} & {(4)}\end{matrix}$where equations (2) and (3) are a result of X(k₁, n), X(k₂, n), and V(n)being uncorrelated, and equation (4) assumes that X(k, n) is 4-QAM(quadrature amplitude modulation). Approximating the expectationoperator with a time-average, H(k₁) can be estimated as

$\begin{matrix}{{{\hat{H}\left( k_{1} \right)} = {\frac{1}{2T}{\sum\limits_{n = 0}^{T - 1}\;{{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)}}}},} & (5)\end{matrix}$Using a similar derivation, H(k₂) can be estimated as

$\begin{matrix}{{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2T}{\sum\limits_{n = 0}^{T - 1}\;{{Y\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)}}}},} & (6)\end{matrix}$with underlying estimator given by

$\begin{matrix}{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2}{{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}.}}} & (7)\end{matrix}$

More precisely (7) can be written as

$\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{E\left\lbrack {{X\left( {k_{2},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}} + {{H\left( k_{1} \right)}{E\left\lbrack {{X\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}}} \right\}}} \\{{= {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{\sigma_{x}^{2}\left( k_{2} \right)}} + {{H\left( k_{1} \right)}{r_{x}\left( {k_{1},k_{2}} \right)}}} \right\}}},}\end{matrix} & (8)\end{matrix}$where σ_(x) ² (k₂) is the energy of the training sequence at tone k₂ andr_(x)(k₁, k₂) is the cross correlation between the sequences transmittedat tones k₁ and k₂. In the ideal scenario of equation (7), σ_(x) ²(k2)=2(for 4-QAM) and, because of the independence assumption, r_(x)(k₁,k₂)=0, therefore, perfect alias channel estimation is possible.Unfortunately, this assumption does not always holds as pseudo randomsequences with poor statistical properties are typically used in realmodems.

A better estimate of the alias channel can be made by first estimatingthe reduced-rate channel, subtract its effect from the received symbols,and then estimate the alias channel. The procedure can be statedmathematically as follows.

Using a derivation similar to the one used for the alias

$\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{1} \right)} = {\frac{1}{2}{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack}}} \\{{= {\frac{1}{2}\left\{ {{{H\left( k_{1} \right)}{\sigma_{x}^{2}\left( k_{1} \right)}} + {{H\left( k_{2} \right)}{r_{X}\left( {k_{1},k_{2}} \right)}}} \right\}}},}\end{matrix} & (9)\end{matrix}$

It is noted that the estimate of H(k₁) is better than the estimate ofH(k₂) because it is assumed that H(k₁)≧H(k₂). This statement can bequalified by identifying the error component of the channel estimates,i.e., the second term in equations (9) and (8).|e_(k) ₁ |² =|H(k ₂)|² |r _(x)(k ₁ ,k ₂)|²,  (10)|e_(k) ₂ |² =|H(k ₁)|² |r _(x)(k ₁ ,k ₂)|²,  (11)

$\begin{matrix}{\frac{{e_{k_{2}}}^{2}}{{e_{k_{1}}}^{2}} = {\frac{{{H\left( k_{1} \right)}}^{2}}{{{H\left( k_{2} \right)}}^{2}}{1}}} & (12)\end{matrix}$

The effect of the reduced-rate channel can be subtracted as follows.Y (k ₁ ,n)=Y(k ₁ ,n)−Ĥ(k ₁)X(k ₁).  (13)

And based on these calculations, the alias channel can be estimated.

$\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2}{E\left\lbrack {{\overset{\_}{Y}\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}}} \\{= {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{\sigma_{x}^{2}\left( k_{2} \right)}} + \left. \left( {\left( {{H\left( k_{1} \right)} - {\hat{H}\left( k_{1} \right)}} \right){r_{x}\left( {k_{1},k_{2}} \right)}} \right. \right\}} \right.}}\end{matrix} & (14)\end{matrix}$

The improvement of this approach over that of equation (8) is quantifiedby comparing the corresponding error energies, i.e.,|e′ _(k2)|² =|H(k ₁)−Ĥ(k ₁)|² |r _(x)(k ₁ , k ₂)|²,  (15)More specifically, the ratio of equations (11) and (15) gives

$\begin{matrix}{\frac{{e_{k_{2}}}^{2}}{{e_{k_{2}}^{\prime}}^{2}} = {\frac{{H\left( k_{1} \right)}}{{{H\left( k_{1} \right)} - {\hat{H}\left( k_{1} \right)}}} > 1.}} & (16)\end{matrix}$

Once the reduced-rate and alias channels have been identified usingeither of the methods proposed above, the noise can be estimated asV(n)=Y(k ₁ ,n)−H(k ₁)X(k ₁ ,n)−H(k ₂)X(k ₂ ,n).  (17)

Using data from time n=0, . . . , T−1, the noise variance can beestimated as

$\begin{matrix}{\sigma_{v}^{2} = {\frac{1}{T}{\sum\limits_{n = 0}^{T - 1}\;{{V(n)}V*{(n).}}}}} & (18)\end{matrix}$

The sub-channel SNR can then be estimated by

$\begin{matrix}{{{{SNR}\left( k_{1} \right)} = \frac{\sigma_{x}^{2}{{H \cdot \left( k_{1} \right)}}^{2}}{\sigma_{v}^{2}}},} & (19)\end{matrix}$where σ_(x) ²=2 for 4-QAM.

An alternate embodiment can utilize a low complexity alias cancellationapproach that is conceptually equivalent to the two stage method forestimating the reduced-rate and aliased channels described previously.This reduced implementation approach uses only one fourth of theavailable data, effectively reducing the memory and computationalrequirements by the same factor.

The low complexity approach implicitly calculates the reduced-ratechannel H(k₁), subtract its effect from the receive signal, and thenestimates the alias channel H(k₂). First, the effect of the receivechannel on the constellation ++ is obtained by averaging received tonescarrying the desired constellation, i.e., X(k₁, n)=1+j. This is,Ŷ ₊₊ ¹(k ₁)=E[Y(k ₁ ,n)]≈H(k ₁)(1+j) with k ₁ , ns.t. X(k ₁,n)=(1+j).  (20)Second, four averages of the received symbols are estimated, this is,

$\begin{matrix}\begin{matrix}{{Y_{++}^{1,2}\left( k_{1} \right)} = {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\mspace{14mu}{with}}} \\{k_{1},{{n\mspace{14mu}{s.t.\mspace{11mu}{X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\mspace{14mu}{and}\mspace{14mu}{X\left( {k_{2},n} \right)}} = \left( {1 + j} \right)}}} \\{{\approx {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {1 + j} \right)}}},}\end{matrix} & (21) \\\begin{matrix}{{Y_{- +}^{1,2}\left( k_{1} \right)} = {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\mspace{14mu}{with}}} \\{k_{1},{{n\mspace{14mu}{s.t.\mspace{11mu}{X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\mspace{14mu}{and}\mspace{14mu}{X\left( {k_{2},n} \right)}} = \left( {{- 1} + j} \right)}}} \\{{\approx {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {{- 1} + j} \right)}}},}\end{matrix} & (22) \\\begin{matrix}{{Y_{+ -}^{1,2}\left( k_{1} \right)} = {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\mspace{14mu}{with}}} \\{k_{1},{{n\mspace{14mu}{s.t.\mspace{11mu}{X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\mspace{14mu}{and}\mspace{14mu}{X\left( {k_{2},n} \right)}} = \left( {1 - j} \right)}}} \\{{\approx {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {1 - j} \right)}}},}\end{matrix} & (23) \\\begin{matrix}{{Y_{--}^{1,2}\left( k_{1} \right)} = {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\mspace{14mu}{with}}} \\{k_{1},{{n\mspace{14mu}{s.t.\mspace{11mu}{X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\mspace{14mu}{and}\mspace{14mu}{X\left( {k_{2},n} \right)}} = \left( {{- 1} - j} \right)}}} \\{{\approx {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {{- 1} - j} \right)}}},}\end{matrix} & (24)\end{matrix}$one for each of the four possible alias constellation X(k₂, n)=±1±j andconditioned to the ++ received point, i.e., X(k₁,n)=1+j. Finally, theeffect of H(k₂) on the received symbol is calculated asY ₊₊ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ₊₊ ^(1,2)(k ₁)≈−H(k ₂)(1+j)  (25)Y ⁻⁺ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁻⁺ ^(1,2)(k ₁)≈−H(k ₂)(−1+j)  (25)Y ⁺⁻ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁺⁻ ^(1,2)(k ₁)≈−H(k ₂)(1−j)  (27)Y ⁻⁻ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁻⁻ ^(1,2)(k ₁)≈−H(k ₂)(−1−j)  (28)

These quantities are subtracted directly from the received frames priorto SNR calculation to cancel the alias component,Y (k ₁ ,n)=Y(k ₁ , n)+Y ₊₊ ²(k ₁) for k ₁ ,n s.t. X(k ₂ ,n)=(1+j)  (29)Y (k ₁ ,n)=Y(k ₁ ,n)+Y ⁻⁺ ²(k ₁) for k₁ ,n s.t. X(k ₂ ,n)=(−1+j)  (30)Y (k ₁ ,n)=Y(k ₁ ,n)+Y ⁺⁻ ²(k ₁) for k ₁ ,n s.t. X(k₂ ,n)=(1−j)  (31)Y (k ₁ ,n)=Y(k ₁ ,n)+Y ⁻⁻ ²(k ₁) for k ₁ ,n s.t. X(k ₂ ,n)=(−1−j)  (32)

One immediate improvement of this approach will be to combine the four“estimates” of the alias channel H(k₂) into a single one. This willrequire rotating the Y_(xx) ² and averaging at the end.

Independently of the method used for alias cancellation, care should betaken when calculating expectations if a training sequence with poorstatistical properties is used. In particular, this is the case for theT1.413 Medley sequence. This limitation can be resolved by consideringthe same number of constellation points for implementing the expectationoperators.

A method of communicating across a channel is shown on FIG. 7. Themethod begins at 700. Information having a known bandwidth and a knownspectrum is received at a receiver having a reduced channel bandwidththat is less than the known bandwidth at 710. At 720, an estimate of areduced-rate channel spectrum 721 is calculated from the receivedinformation. At 730, the reduced-rate channel spectrum 20 is subtractedfrom the known spectrum 24. At 740, the received information is modifiedbased upon the aliasing spectrum 24. The method ends 750.

So far, the present invention has been described in the context of anADSL modem using DMT modulation scheme. It is noted, however, that theinvention can be applied to a great number of other applications.Basically, any multi-tone communication systems could benefit from thisinvention.

While this invention has been described with reference to illustrativeembodiments, this description is not intended to be construed in alimiting sense. Various modifications and combinations of theillustrative embodiments, as well as other embodiments of the invention,will be apparent to persons skilled in the art upon reference to thedescription. It is therefore intended that the appended claims encompassany such modifications or embodiments.

1. A method of communicating across a channel, the method comprising:receiving information having a known bandwidth and a known spectrum, theinformation being received at a receiver having a reduced channelbandwidth that is less than the known bandwidth; calculating an aliasingspectrum based on the known spectrum and the frequency differencebetween the known bandwidth and the reduced-channel bandwidth; andmodifying the received information based upon the aliasing function tocompensate for alias distortion, wherein calculating an aliasingspectrum comprises: estimating a reduced-rate channel spectrum from thereceived information; and subtracting the reduced-rate channel spectrumfrom the known spectrum.
 2. The method of claim 1 wherein calculating analiasing spectrum comprises calculating the aliasing spectrum directlyfrom the known spectrum.
 3. The method of claim 1 wherein the receivedinformation comprises 4-QAM information.
 4. The method of claim 1wherein modifying the received information comprises estimating acompensated signal-to-noise ratio within the reduced-channel, thecompensated signal-to-noise ratio being estimated to reduce the effectof the aliasing spectrum.
 5. The method of claim 1 wherein the receivedinformation comprises a multicarrier modulated signal.
 6. The method ofclaim 5 wherein the received information comprises a discrete multitone(DMT) modulated signal.
 7. The method of claim 5 wherein calculating analiasing spectrum comprises: selecting a constellation having a numberof symbol; averaging received tones carrying the constellation;estimating an average received symbol for each symbol in theconstellation; and modifying the received information based the averagereceived symbols.
 8. A method of initializing a communication channel,the method comprising: receiving a multicarrier modulated signal havingsubcarriers at each of a number of frequencies over a particularbandwidth, the multicarrier modulated signal including a plurality ofknown training symbols; estimating an alias signal-to-noise ratioattributable to an aliasing spectrum based upon the known trainingsymbols; estimating a reduced-channel signal-to-noise ratio for each ofthe subcarriers, the reduced channel signal-to-noise ratio beingestimated using the alias signal-to-noise ratio; and determining ausable portion of the communication channel based upon thereduced-channel signal-to-noise ratio.
 9. The method of claim 8 andfurther comprising communicating the reduced-channel signal-to-noiseratio to a second communication device across the communication channel.10. The method of claim 8 wherein the multicarrier modulated signalcomprises a discrete multitone modulated signal.
 11. The method of claim8 wherein the communication channel comprises a digital subscriber line(DSL).
 12. The method of claim 11 wherein the communication channelcomprises an asymmetric digital subscriber line.
 13. The method of claim11 wherein the multicarrier modulated signal is received at the remoteunit on a DSL system.
 14. The method of claim 8 wherein estimating analias signal-to-noise ratio comprises calculating a aliassignal-to-noise ratio directly from the known training symbols.
 15. Themethod of claim 14 wherein estimating an alias signal-to-noise ratiocomprises: estimating a reduced-rate channel spectrum from the receivedsignal; estimating an alias channel spectrum from the received signal;and estimating noise attributable to the alias channel basedreduced-rate channel spectrum and the alias channel spectrum.